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\documentclass{acmabs}

\begin{document}

\Journal{Journal of the ACM}

\refkey{NebelB95}

\title{Reasoning About Temporal Relations: A Maximal Tractable Subclass of
  {Allen's} Interval Algebra}

\author{Bernhard Nebel \and Hans-J{\"u}rgen B{\"u}rckert}

\Pages{43--66}

\Month{January}

\Year{1995}

\Volume{42}

\Number{1}

\maketitle

\begin{abstract}

We introduce a new subclass of Allen's interval algebra we call ``ORD-Horn
  subclass,'' which is a strict superset of the ``pointisable subclass.'' We
  prove that reasoning in the ORD-Horn subclass is a polynomial-time problem
  and show that the path-consistency method is sufficient for deciding
  satisfiability. Further, using an extensive machine-generated case analysis,
  we show that the ORD-Horn subclass is a maximal tractable subclass of the
  full algebra (assuming $\mathrm{P} \ne \mathrm{NP}$). In fact, it is the
  unique greatest tractable subclass amongst the subclasses that contain all
  basic relations.

\end{abstract}

\begin{categories}

F.2.2[sequencing and scheduling]; I.2.4[relation systems]

\end{categories}

\begin{terms}

Algorithms, Theory

\end{terms}

\begin{keywords}

Constraint satisfaction, interval algebra, qualitative reasoning, temporal
  reasoning

\end{keywords}

\end{document}
